Problem: What do the following two equations represent? $-2x+2y = 5$ $-10x-10y = 5$
Answer: Putting the first equation in $y = mx + b$ form gives: $-2x+2y = 5$ $2y = 2x+5$ $y = 1x + \dfrac{5}{2}$ Putting the second equation in $y = mx + b$ form gives: $-10x-10y = 5$ $-10y = 10x+5$ $y = -1x - \dfrac{1}{2}$ The slopes are negative inverses of each other, so the lines are perpendicular.